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# Doubts about the integrated finite difference method (IFDM)

Hello everyone,

I am conducting a comparative study between the TOUGH and DARTS simulators. I went through the basic documentation to understand how both simulators work, especially about the discretization scheme.

From what I understand, TOUGH uses IFDM, which is a finite volume method or FVM (although the name might suggest it is a FDM). On the other hand, DARTS also applies an FVM using two-point and multi-point flow approximation (TPFA and MPFA respectively). Since both are FVMs, they both work on the integral form of the governing equations and must be conservative with respect to the physical quantities.

My question is: Is IFDM a type of FVM or is it the most general approach? What would be the basic difference compared to the TPFA used in DARTS?

Reading about IFDM in the original article, it seemed to me to be the most general approach of a FVM. I also found in some references that the TPFA is generally used as the simplest example of a FVM, but it doesn't mention the constraints that usually related to the IFDM: The interfaces between elements must be perpendicular to the line joining two nodal points and should cross that line at their midpoint (as much as possible).

• Staff Scientist
• Christine_Doughty
• 2 wk ago
• Reported - view

Hello Luis,

The IFDM is a finite volume method. It is described in the TOUGH2 User's manual (Pruess et al., 2012), which may be viewed or downloaded from the TOUGH Manuals web page (https://tough.lbl.gov/documentation/tough-manuals/). See Section 5.2 and Appendix B. TOUGH uses a two-point flow approximation.

More details on the IFDM are available in Narasimhan, T.N. and Witherspoon, P.A., An integrated finite difference method for analyzing fluid flow in porous media, Water Resources Research, 12(1), 1976, and Edwards, A.L., TRUMP: A computer program for transient and steady state temperature distributions in multidimensional systems, National Technical Information Service, National Bureau of Standards, Springfield, Va., 1972.  If you have trouble obtaining either of these publications, let me know and I will email you PDFs.

I don't know DARTS, so I can't comment on how the IFDM compares to its spatial discretization method.

Best wishes, Christine

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